Dynamic Capital Allocation With Distortion Risk Measures

Tsanakas and Barnett (2002) employed concepts from cooperative game theory (Aumann and Shapley, 1974) for the allocation of risk capital to portfolios of pooled liabilities, when distortion risk measures (Wang et al., 1997) are used. In this paper we generalise previously obtained results in three directions. Firstly, we allow for the presence of non-linear portfolios. Secondly, based on the concept of correlation order (Dhaene and Goovaerts, 1996) we proceed with discussing the links between dependence structures, capital allocation and pricing, as well as dropping a restrictive assumption on the continuity of probability distributions. Finally, we generalise the capital allocation methodology to a dynamic setting and conclude with a numerical example.

[1]  Jan Dhaene,et al.  Comonotonicity, correlation order and premium principles , 1998 .

[2]  Dirk Tasche,et al.  Risk contributions and performance measurement , 2000 .

[3]  G. Choquet.  Theory of capacities , 1954 .

[4]  Jean-Pierre Aubin,et al.  Cooperative Fuzzy Games , 1981, Math. Oper. Res..

[5]  Shaun S. Wang,et al.  Axiomatic characterization of insurance prices , 1997 .

[6]  M. Yaari.  The Dual Theory of Choice under Risk , 1987 .

[7]  Marc Goovaerts,et al.  Dependency of Risks and Stop-Loss Order , 1996, ASTIN Bulletin.

[8]  Dieter Denneberg.  Conditioning (updating) non-additive measures , 1994, Ann. Oper. Res..

[9]  Dieter Denneberg,et al.  Conditional expectation for monotone measures, the discrete case , 2002 .

[10]  L. Shapley,et al.  Values of Non-Atomic Games , 1974 .

[11]  Virginia R. Young.  Families of update rules for non-additive measures: Applications in pricing risks , 1998 .

[12]  A. Tsanakas,et al.  Risk Capital Allocation and Cooperative Pricing of Insurance Liabilities , 2003 .

[13]  P. Walley.  Statistical Reasoning with Imprecise Probabilities , 1990 .

[14]  Xiongzhi Chen.  Brownian Motion and Stochastic Calculus , 2008 .

[15]  Nicos Christofides,et al.  Risk Exchange with Distorted Probabilities , 2006, ASTIN Bulletin.

[16]  A. Chateauneuf,et al.  Choquet Pricing for Financial Markets with Frictions , 1996 .

[17]  D. Tasche.  Conditional Expectation as Quantile Derivative , 2001, math/0104190.

[18]  D. Schmeidler.  Subjective Probability and Expected Utility without Additivity , 1989 .

[19]  P. Embrechts,et al.  Risk Management: Correlation and Dependence in Risk Management: Properties and Pitfalls , 2002 .

[20]  M. Denault.  Coherent allocation of risk capital , 2001 .

[21]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[22]  Virginia R. Young,et al.  Risk-adjusted credibility premiums using distorted probabilities , 1998 .